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Distribution authorized to U.S. Gov't. agenciesand their contractors; Critical Technology; 22JUL 1970. Other requests shall be referred toDefense Advanced Research Projects Agency,Attn: TIO, 675 North Randolph Street,Washington, DC 22203-2114. This documentcontains export-controlled technical data.
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AFTAC Project No. VELA/T/0701/B/ASD
ID Oi ^^ Technical Report No. 5
SEISMIC ARRAY PROCESSING TECHNIQUES
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NOISE STUDY FOR TFO EXTENDED SHORT-PERIOD ARRAY
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, Prepared by
Thomas W, Rekieta
Stanley J. Laster, Project Scientist Frank H. Binder, Program Manager
Area Code 214, 238-6521
TEXAS INSTRUMENTS INCORPORATED Services Group P.O. Box 5621
Dallas, Texas 75222
Contract No. F3365J-70-C-0100 Amount of Contract: $339,052
Beginning 15 July 1969 Ending 14 July 1970
D D C
^ OCT 5 1970
Lijjrnr.v-Trrrm
^ Prepared for
AIR FORCE TECHNICAL APPLICATIONS CENTER Washington, D. C. 20333
Sponsored by
ADVANCED RESEARCH PROJECTS AGENCY Nuclear Monitoring Research Office
ARPA Order No. 624 ARPA Program Code No. 9F10
22 July 1970
1 I
Acknowledgm»nt: ThU roearch was •upporied by th« Advanced Reraarch Project« Agency, Nuclear Monitoring Re tea rch Office, under Project VELA-UNIFORM, and accomplished ander the technical direction of the Air Force Technical Applications Center under Contract No. FU6S7-7O-C-0IOO.
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NOISE STUDY FOR TFO EXTENDED SHORT-PERIOD ARRAY
Technical Report No. 5
SEISMIC ARRAY PROCESSING TECHNIQUES
, Prepared by
Thomas W. Rekieta
Stanley J. Laster, Project Scientist Frank K. Binder, Program Manager
Area Code 214, 238-6521
TEXAS INSTRUMENTS INCORPORATED Services Group P.O. Box 5621
Dallas, Texas 75222
Contract No. F336E7-70-C-0100 | Amount of Contract: $339,052
Beginning 15 July 1969 Ending 14 July 1970
Prepared for
AIR FORCE TECHNICAL APPLICATIONS CENTER Washington, D. C. 20333
Sponsored by "
ADVANCED RESEARCH PROJECTS AGENCY Nuclear Monitoring Research Office
ARPA Order No. 624 ARPA Program Code No. 9F10
22 July 1970
Acknowtedgmcnt: This research was supported b? the Advanced Research Projects Agency, Nuclear Monitoring Research Office, under Project VELA-UNIFORM, and accomplished under the technical direction of the Air Force Technical Applications Center under Contract No. F33657-7O-C-0IO0.
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1
This document is subject to special export controls and each transmittal to foreign governments or foreign nationals may be made only with prior approval of Chief, AFTAC.
Qualified users may request copies of this document from:
Defense Documentation Center Cameron Station
Alexandria, Virginia 22314
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1 1 1 I I
TABLE OF CONTENTS
Section Title Page 2
ABSTRACT vi
I INTRODUCTION I-1
II SUMMARY AND CONCLUSIONS II-1
A. ANALYSIS OF THE AMBIENT NOISE FIELD 11-1 B. ANALYSIS OF MCF PERFORMANCE U-J»
III PREPARATION OF DATA FOR ANALYSIS III-l
A. EDITING OF DATA III-l B. DEVELOPMENT OF X-POWER MATRICES III-3
1. 'Summer1 Data 111-4 2. 'Winter' Data 111-4
C. POLARITY REVERSAL PROBLEM 111-4
IV ANALYSIS OF AMBIENT NOISE FIELDS IV-1
A. SINGLE-CHANNEL POWER-DENSITY ANALYSIS IV-1 B. HIGH-RESOLUTION FREQUENCY WAVENUMBER IV-4
ANALYSIS 1. 'Summer' Surface-Mode Spectra IV-6 2. 'Summer' P-Wave Spectra IV-11 3. 'Winter' Surface-Mode Spectra IV-14 4. 'Winter' P-Wave Spectra IV-16
C. K-LINE SPECTRAL ANALYSIS IV-22
V. MULTICHANNEL FILTER DESIGN AND EVALUATION V 1
A. MCF DESIGN V-l B. EVALUATION OF MCFs V-2
1. Signal-to-Noise Improvements V-2 C. WAVENUMBER ANALYSIS OF MCF RESPONSES V-5 D. CONCLUSIONS V-10
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LIST OF ILLUSTRATIONS
Figure Figure Page
III-l Extended Short-Period Array at TFO 111-2
III-2 Spectra Illustrating Effects of Anti-Alias £. .d Pre- UI-3 Whitening Filter
III-3 Spectra Window of the Crosspower Matrix Computed III-5 from the TFO Noise Samples
iv. 1 Single-Channel Power Density Spectra from 'winter1 IV-2 Recording Period
IV-2 Single-Channel Power Density Spectra from 'summer' IV-3 Recording Period
IV-3 Comparison of 'winter' and 'summer' Single-Channel IV-5 Power Density Spectra
IV-4 High Resolution Wavenumber Spectra of . 169 and .203 IV-7 Hz 'summer' Noise
rV-5 High Resolution Wavenumber Spectra of .23 and .27 Hz IV-8 'summer' Noise
IV-6 High Resolution Wavenumber Spectra of . 304 and . 338 IV-9 Hz 'summer' Noise
IV-7 High Resolution Wavenumber Spectra of . 372 and .405 IV-IO Hz 'sxunmer1 Noise
IV-8 High Resolution Wavenumber Spectra of 'summer' IV-12 P-Wave Noise at . 507 and .541 Hz
IV-9 High Resolution Wavenumber Spectra of 'summer' IV-1,^ P-Wave Noise at . 574 and . 608 Hz
IV-10 High Resolution Wavenumber Spectra of the . 12 Hz IV-15 'winter' Noise
IV-11 High Resolution Wavenumber Spectra of . 163 and .203 IV-17 Hz 'winter' Noise
IV-12 High Resolution Wavenvunber Spectra of . 244 and . 284 IV-18 Hz 'winter' Noise
IV-13 High Resolution Wavenumber Spectra of .33 and .407 IV-19 Hz 'winter' Noise
IV-14 High Resolution Wavenumber Spectra of the 'winter' rV-20 P-Wave Noise at Frequencies of .41 and .49 Hz
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IV-15
IV-16
IV-17
IV-18
V-l
V-2
V-3
V-4
V-5
LIST OF ILLUSTRATIONS (CONT'D)
Title Page
High Resolution Wavenumber Spectra of the 'winter' IV-21 P-Wave Noise at Frequencies of . 57 and .61 Hz
K-Line and Integrated Spectra of 'winter' Data IV-24 Recorded from the Extended Short-Period Array
K-Line and Integrated Spectra of 'summer' Data IV-26 from the Extended TFO Array
Distribution of Ambient Noise Power for Identified IV-29 Sources
Signal-to-Noise Improvement Obtained by MCF V-3 Processing on 'summer' and 'winter' Data
Signal-to-Noise Improvement of MCFs Relative to V-4 Beamsteer Processing of Similar Elements
Wavenumber Response of 'summer' MCF at Frequencies V-7 of . 135 and . 169 Hz
Wavenumber Response of 'summer' MCF at Frequencies V-8 of . 236 and . 304 Hz
Wavenumber Response of 'winter' MCF at Frequencies V-9 of . 122 and .249 Hz
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ABSTRACT
Seismic data was digitally collected from the recently extended
short-period array of the Tomo Forest Observatory during the summer of 1968
and the winter of 1969. An analysis of the data was made to characterize the
ambient noise field from each period and to determine time-and space-station-
arity of the fields. The effectiveness of multi-channel filter processing on
the extended array was also measured.
Several contributors to the ambient noise field could be defined
in both of the periods analyzed and appeared to be both time-^ind space-station-
ary. Other contributors, due primarily to atmospheric storm or pressure
activity, were not stationary and could be related to its generating source.
Multi-channel filtering of the extended array could not provide
any significant improvement over simple beamsteering at frequencies of interest
(greater than . 8 Hz). At lower frequencies, the amount of improvement obtained
by MCF processing relative to beamsteering was directly related to the increase
in noi.«e level due to the non-stationary contributor of the noise field.
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SECTION I
INTRODUCTION
Two data collection efforts were conducted at TFO for the pur-
pose of recording high quality digital data from the recently extended short-
period array and the three componenl long-period array. The data collected
were classified as 'summer' data, consisting of the data collected during the
pe-iod of 6 June to 21 June 1968, and as 'winter' data, which was recorded
during the period of 27 January to 4 March 1969.
This report covers the TFO extended short-period array noise
study. The primary objectives of the task were to compare the 'summer' and
'winter' noise field characteristics, to estimate the time and spacial stationärity
of these noise fields, and to establish the effectiveness of multichannel process-
ing using the extended array.
The analysis of the ambient noise field and the effectiveness of
multichannel processing on the array outputs was conducted almost exclusively
in the frequency domain using crosspower matrices developed from noise
samples selected from each of the recording periods. A summary of the analysis
and conclusion are presented in the next section. A detailed description of the
processing and analysis of the data is presented in following sections.
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SECTION II
', *'* SUMMARY AND CONCLUSIONS ,- > - ,
The ambient'noise field of the extended short-period array at s ■ \
TFO was characterized from a spectral analysis of data samples selected
from each of the recording periods. The time- and space-stationary of the
coherent noise energy was measured from absolute.-«ingle channel power-
density spectra and from high resolution wavenumber spectra. The effective- . ■ »
ness of multichannel processing on the extended array was determined from i ' • /■
the design and Evaluation of MCFs on crosspower matrices of data from each
of the periods being analyzed.
A. ANALYSIS OF THE AMBIENT NOISE FIELD
Absolute level of the ambient noise field was determined from
single-channel power density spr, a, computed by the Markov technique.
Significant changes in the absolute level of the power frequency energy were
evident. The 'winter' samples showed a general increase in the absolute power
level especially at frequencies below .25 Hz. The increases in the absolute
levels of the power spectra appeared to be directly related to the amount and
intensity of atmospheric pressure activity observed from weather maps. A
significant increase in energy is observed in the area of . 12 Hz during a
•winter1 period of very intense atmospheric disturbance off the Alaskan Coast. *
The spacial organization of the coherent noise energy during
the winter and summer period was determined from high resolution frequency-
wavaftumber spectra computed for each of the periods.
Surface mode energy from the Northeast is observed during both
periods. This energy is observed with the fundamental surface node velocity
of approximately 3. 2 km/second at frequencies below . 25 Hz. At higher fre-
quencies this energy appears to travel at a higher velocity of approximately 3. 6
km/second indicating the existence of higher-order surface mode energy.
v
* Burg, J.P. , "Maximum Entropy Spectral Analysis" Society of Exploration Geophysicists
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At frequencies of . 4 Hz and greater the spacial organization of
the coherent surface mode energy becomes isotropic in nature. At these fre- „
quencies a significant amount of P-wave energy from the South, with very high
apparent horizontal velocities (40 km/second or greater) are consistently
observed. Secondary P-wave contributions from the Northeast and Northwest
with slightly lower apparent horizontal velocities are also observed.
The most significant difference in the spacial organization of the
summer and winter ambient noise is the addition of noise from the Northwest
as observed in the winter noise sample. At .12 Hz, the surface mode energy
from this direction dominates the spectra. However, as the frequencies increase,
the surface mode energy contribution from this direction rapidly decreases. The
P-wave energy from the Northwest continues to be a significant contributor to the
noise field up to frequencies of approximately . 5 Hz. Analysis of the measured
apparent horizontal velocity of the P-wave energy from the Northwest indicates
the Alaskan storm to be the generating source.
A slight increase in the surface mode energy from the South and
Southwest is also observed in the 'winter' data. In general the increase in the
surface mode energy relates very well to the pressure activity in the correspond-
ing direction.
High-resolution K-line spectra were computed to determine the
relative contribution of each noise source to the total ambient noise power. The
percent contributed as P-wave, directional surface mode, and isotropic surface
mode is illustrated in Figure IV-IS.
Based on the spectral analysis of the noise from the two time
periods the spatial organization of certain components of the coherent noise
field, surface-mode energy from the Northeast and P-wave from the South,
are stationary. However, the other surfac«-mode and P-wave components,
which are highly influenced by seasonal and daily atmospheric variations or
distrubances, are not time or space stationary.
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B. ANALYSIS OF MCF PER FOP MANCE
) / A set of multichannel filters were designed from a crosspower
matrix computed from a long noise sample fron, each of the time periods. The
signal-to-noise in^provement was determined from a frequency domain appli-
cation of the MCF to the noise and signal crosspower matrices used in the
design. Results were compared to a similar applicaton of a simple beamsteer
(straight summation) process to the same matrices. \
Using 34 elements of the extend short-period array a S/N improve-
ment of 23 db was obtained by MCF processing at the frequency of . 12 Hz on the
•winter1 data. Wa''. enumber analysis of MCF response shows this to be due
primarily to the rejection of the surface-mode energy fro _ the Northwest.
In general, some S/N improvement can be obtained by MCF pro-
cessing over that of beamsteering at frequencies below . 75 Hü. On the »summer'
data, S/N improvements of 3 to 6 db alcove that of the beamsteering processing
was obtained by MCF processing. Additional gain is obtained on noise samples
which have an increase in coheren* energy at these frequencies due to the pre-
viously discussed atmospheric activity. However, since the generating source is
not considered as space stationary, on line processing with fixed MCFs is not
expected to provide any significant improvement. At frequencies above .8 Hz,
MCF processing of the extended array would not provide any significant signal-
to-noise improvement over beamsteering even under stationary conditions.
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SECTION m
PREPARATION OF DATA FOR ANALYSIS
Large quantities of seismic data were collected from the extended
short-period array on a Digital Field System (DFS) operated by Texas Instru-
ments' engineers during two recording efforts. The first recording session
covered the period of 6 June 1968 to 21 June 1968. Data from this period will
be designed as 'summer' data. The second recording period, during which
'winter' data were recorded covered the period from 27 January 1969 to 3 March
1969. This section outlines the pre-processing performed on noise samples
selected from the recorded data for extensive analysis. For reference. Figure
III-l shows the relative locations of the extended short-period array elements
from which the data was collected.
A. EDITING OF DATA
The 'summer' data was recorded during a period when severe
spiking problems on array elements were being experienced on the recently
extended array. Several segments of the data, covering approximately two
hours, were selected and edited from the field tapes. One of these samples
recorded on 19 June 1968, containing 33 channels of seismic data (elements
Z32, Z6, Z18, and Z20 were inoperative) was then processed with a program
to detect and remove the undesired spikes from the data.
The data was recorded by the DFS with a sampling interval of
.096 seconds. Since the noise energy at the higher frequencies (greater than
1.5 Hz) was expected to be random across the extended array due to the large
interelement spacing, the data was high-cut (anti-aliased) filtered and resampled
to provide a sampling interval of .288 seconds and a frequency band of 0 - 1.736
Hz. The data was also pre-whitened as shown by Figure 111-2.
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Figure III-l. Extended Short-Period Array at TFO
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-12 -
-24
ORIGINAL SPECTRA
AFTER APPLICATION OF ANTIALIAS AND PREWHITENING FILTER
X _L _L _L _L 0.25 0.50 0.75 1.00
FREQUENCY CHz)
1.25 1.50 1.75
Figure III-2. Spectra Illustrating Effects of Anti-Alias and Pre-Whitening Filter.
Similarly, several segments of data were edited from the 'winter'
data tapes. One of the noise samples recorded on 27 february 1969 during which
intense low pressure conditions were observed from weather maps, was selected
for a detailed analysis. However, due to bad spots in the data such as missing
elements and severe spiking,only 50 minutes of data from any recording was
acceptable for analysis. All but three (Z19, Z22, and Z31) of the 37 arrav
elements were operating satisfactorily. The data was anti-aliased filtered and
resampled to provide the .288 second sampling interval.
B. DEVELOPMENT OF X-POWER MATRICES
The fast Cooley-Turkey transform method was used to obtain the
frequency domain representation of the 'summer' and 'winter' noise samples.
The crosspower matrices were developed for each of the noise samples as
follows.
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1. •Summer' Data
The time traces of the 'summer' data was transformed using
gates of 512 points of data at a time. A total of 45 gates were transformed.
Crosspower matrices for the 33 channels of data were computed from the trans-
forms for each of the 257 frequencies covering the band 0. 0 to I. 736 Hz in
.00678 Hz increments. The matrices were then stacked for all the transform
gates and smoothed across frequencies by an equal weighting function for five
adjacent frequencies. Every fifth frequency was saved for further analysis re-
sulting in a set of 51 matrices for the 0-1.736 Hz band at a frequency incre-
ment of .0339 Hz between matrices. The spectral window due to the transform
gate and smoothing described is shown in Figure III-3.
2. 'Winter' Data
The 'winter' time traces were transformed in 256 point segments
resulting in 129 complex frequency values for the 0 to 1.736 Hz frequency band.
A total of 40 segments were transformed for the 34 channels of data. Cross-
power matrices were computed from the transforms and stacked. In this case,
smoothing of the matrices was performed across three adjacent frequencies
with equal weighting of matrices. This resulted in a set of 43 matrices covering
the frequency band of the data in .041333 Hz increments. The effective spectral
window for this data is also shown in Figure III-3.
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SECTION IV
ANAT YSIS OF AMBIENT NOISE FIELDS
The characteristics of the 'winter1 and 'summer' noise field
were determined and compared through an analysis of single channel-power
density spectra, frequency-wavenumber spectra and K-line spectra for the
extended short-period array. The time- a.r.d space-stationärity of the noise
field were estimated from the noise samples analyzed.
A. SINGLE-CHANNEL POWER-DENSITY ANALYSIS
Power density spectra were estimated, using the Markov Spectral
Estimation Technique for several channels from each of the noise samples
studied.
The daily i.O Hz calibration of the array seikBora were recorded
by the DFS and used in this study to establish absolute levels for the spectra.
The resulting spectra for the 'winter1 and 'summer' data are shown in Figures
rV-1 and IV-2 respectively.
A comparison of the spectra show an increase of approximately
6 db in noise power for the 'winter' sample across all frequencies shown. A
larger power increase of approximately 12 db is observed in the area of .25 Hz.
During the period which the 'winter' data was recorded, intense
lows occurred at several locations along the coast lines. The strongest of these
were situated off the west coast of Alaska. Others existed along the west coast
of continental U.S., west coast of Mexico, Gulf of Mexico, in the Baffin Bay,
east coast of Greenland, and along the eastern coast line of U.S. near the New
England states. The 'summer' sample used in the analysis was recorded during
a period of relative little storm activity. However, another 'summer' noise
sample was selected for the single-channel-spectral analysis, which was recorded
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during a period when some intense atmospheric activity was occurring off the
Newfoundland coast. This sample 10 June, will be classified as 'noisy summer*
data. A comparison of the spectra from the 'winter' and two 'summer' data sam-
ples is presented in Figure IV-3. The 'noisy summer' sample, has a compara-
ble noise level to the 'winter' data in the . 3 to 1. 0 Hz frequency band. It does
not show the large increase in noise energy below . 3 Mz as observed in the
'winter' data. The following wavenumber analysis will show this increase in
energy below . 3 Hz in the 'winter' noise to be due primarily to the intense low
pressure activity off the Alaskan coast.
B. HIGH-RESOLUTION FREQUENCY WAVENUMBER ANALYSIS
The crosspower matrices, <t>, developed in Section III for each
of the noise samples were used to compute high-resolution wavenumber spectra
at frequencies in the . 12 to .6 Hz band. Spectra from higher frequencies become
difficult to interprete due to the spacial alaising of the array. The method used
to compute the spectra is described by:
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Vis the column vector
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where a is a positive non-zero value.
I. 'Summer' Surface-Mode Spectra
Higb-resolution wavenumber spectra computed at the frequencies
of.169, .203, .236, .270, .304, .338, .372, and .405 Hz from the 'summer •
noise matrices are <*hown in Figure IV-4 through IV-7. The edge velocity of
each of the spectra is 2. 0 km/second. A dashed circle is shown on the spectra
to illustrate the approximate velocity of surface mode energy.
In the first figure, the surface mode energy from the Northwest
appears to be a principal contributor to the noise field along with the P-wave
energy from the South. Measurements of the surface mode peak indicates an
apparent velocity across the array of 3. 17 km/second, A secondarv surface
mode peak at approximately the same velocity is obs&t^ed from the Southwest.
As the frequencies are increased the surface mode peaks rapidly
decrease in relative power and thep-wave from the south becomes predominant.
The surface mode energy becomes very isotropic in nature with a measured
velocity of 3. 2 km/Zsecond. There is continued evidence of directional surface
mode energy from the Northeast at the higher frequencies, however, the apparent
velocity is somewhat higher than that previously measured for the directional
contribution and that of the isotropic noise indicating that it is traveling as
some higher order mode energy.
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Figure IV-4. High Resolution Wavenumber Spectra of . 169 and . 203 Hz 'summer' Noise
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Figure IV-5. High Revolution Wavenumber Spectra of .23 and .27 Hz 'summer' Noise
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Figure IV-6. High Resolution Wavenumber Spectra of . 304 and . 338 Hz •summer1 Noise
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Figure IV-7. High Resolution Wavenumber Spectra of .372 and .405 Hz v •summer' Noise
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The energy arriving from the Northeast is believed to be gen-
erated in the area of Newfoundland and the eastern coast of Canada and the US
based on the spacial organization of P-wave energy and the correlation of atmo-
spheric activity in this region to increased surface mode noise from this direction.
The path of such surface mode noise would transverse the Rocky Mountain region
which could possibly cause the higher order mode energy observed at the higher
frequencies. That is the higher-mode excitation might have been effected by the
fundamental mode impinging on the discontinuity of the mountainous range.
2. 'Summer1 P-Wave Spectra
At the higher frequencies the resolution of the array becomes
sufficient to show the P-wave noise field consists of several contributors. In
an effort to analyze the P-wave noise in detail, wavenumber spectra with an
edge velocity of 10. 0 km/second were computed and are shown in Figures IV-8
and IV-9 for the frequencies of .507, .541, .574, and .608 Hz.
As observed in these spectra the principle p-wave contribution
is from the south with an apparent horizontal velocity of 30 to 40 km/second.
As the frequencies increase, the direction of this energy shifts slightly from
east to west.
A contributor to the p-wave field is also shown in the same direc-
tion as the earlier observed sui face mode energy from the Northeast. Weather
maps of this period show low pressure activity near the southern tip of Green-
land. Events occurring in this area would arrive at TFO with an azimuth of 31
degrees and an apparent horizontal velocity of 15. 5 km/second. The average
velocity and azimuth of the Northeast peak in Figure IV-9 is 15 km/second and
40 degrees, respectively, indicating generating source to be in general area of
the atmospheric activity.
Similarly, the p-wave contribution from the Northwest can be
related to low pressure activity below Alaska, The azimuth of the energy peak
in the wavenumber spectra is measured to be approximately 315 degrees and
the velocity range is 11. 3 to 15. 8 km/second. An event occurring off the
Southern coast of Alaska in the area of the storm activity would arrive at TFO
with an azimuth of 323 degrees and a velocity of 12.4 km/second.
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Figure IV-8. High Resolution Wavenumber Spectra of 'summer1 P-Wave Noise at . 507 and .541 Hz
IV-12 •ervic«s group
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Figure IV-9. High Resolution Wavenumber Spectra of 'summer' P-Wave Noise at . 574 and .608 Hz
7
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3. 'Winter' Surface-Mode Spectra
Analysis of the single-channel power density spectra showed
significant energy increase at very low frequencies in the 'winter' sample.
A high resolution wavenumber spectra computed at the frequency of . 12 Hz
(Figure IV-10) indicates this increase resulted primarily from a strong
surface-mode energy contribution from the Northwest in the direction of the
previously mentioned intense low pressure disturbance off the Western coast
of Alaska. However the high resolution technique also indicates a second
peak in the spectra at this frequency is I 80 to the previous one and is at a
somewhat lower velocity. An analysis of wavenumber spectra computed by
conventional methods were compared to the high resolution spectra to estab-
lish authenticity for each of the observed energy lobes. Conventional spectra
computed at . I 2 Hz gaye no indication of noise energy from the direction of
this second lobe. It is more likely due to effects resulting from the strong
highly coherent noise source from the Northwest. Similar effects have been
observed in wavenumber responses of MCF's designed using noise statistics
consisting of a single highly coherent noise component. At the higher fre-
quencies, the percentage of the total coherent noise energy contributed by a
single source is significantly less than that observed for the Northwest com-
ponent at . I 2 Hz, thereby restricting such effects.
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Figure IV-10. High Resolution Wavenumber Spectra of the . 12 Hz 'winter* Noise
In Figure IV-ll the wavenumber spectra for the frequencies of
. 163 and .203 Hz are shown, in which additional surface mode lobes, similar
to those observed in the 'summer' sample, are evident. The multiple surface
mode lobes are in close agreement with expectations based on the numerous
atmospheric disturbance observed from weather maps.
At the higher frequencies of .24 to .41 Hz (Figures IV-12 and
IV-13), the generating source to the Northeast of the array becomes the princi-
ple contributor to the surface-mode energy as previously observed in the
'summer' data. However, the principle p-wave contributor for the 'winter'
noise is from the Northwest (Alaskan activity) contrary to the predominant
Southern P-wave cortributor in the 'summer' data.
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4. »Winter1 P-Wave Spectra
H;gh resolution wavenumbe.' spectra were computed with an edge
velocity of 10 km/second at the higher frequencies of .41, ,49, .57, and .61 Hz
to determine the spacial structure of the 'winter1 p-wave. These spectra are
shown in Figure IV-14 and IV-15.
At .41 Hz the predominant contributor of p-wave is observed to
be from the Northwest and a secondary contribution from the South. As the
frequencies are increased the Southern contribution continually increases in
relative energy contributi "a over that of the Northwest source.
The average velocity and azimuth of the p-wave energy from the
Northwest was measured from the four spectra to be 15. 3 km/second and 320
degrees. P-wave energy originating in the area of the atmospheric activity
near the Western coast of Alaska vould arrive at TFO with an apparent hori-
zontal velocity of 13. 9 km/second and an azimuth of^ 326 degrees.
As in the 'summer' data, the p-wave energy due to the Southern
contribution has a very high apparent horizontal velocity of 40 km/second or
higher. A possible generating source of the p-wave energy from the South could
not be defined.
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Figure IV-11. High Resolution Wavennmber Spectra of . 163 and . Z03 Hz 'winter' Noise
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Figure IV-12. High Resolution Wavenumber Spectra of .244 and .284 Hz 'winter1 Noise
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Figure IV-13. High Resolution Wavenumber Spectra of . 33 and .407 Hz •winter' Noise
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Figure IV-14. High Resolution Wavenumber Spectra of the 'winter1
P-Wave Noise at Frequencies of .41 and . 49 Hz
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Figure IV-15. High Resolution Wavenumber Spectra of the 'winter' P-Wave Noise at Frequencies of . 57 and . 61 Hz
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C. K-LINE SPECTRAL ANALYSIS
The 1-dimensional wavenumber (K-line) spectra presented and
analyzed in this section can be interpreted as the physical projections of the
2-dimensional power density wavenumber spectra, similar to that discussed
in previous subsection, onto axes which are parallel to some line of array
sensor. The 3-lines of approximately equally-spaced sensors used in this
study is illustrated as arms in Figure UI-l. The resulting K-line spectra for
each line gives the power density of the ambient noise as a function of its
apparent wavenumber along that line. A more detailed discussion of the K-line
spectral technique has been published in a special report on K-line spectral
analysis using the TFO cross-array.
The basic input data for calculating the K-line spectra in the
crosspower matrix, I N..(f) [ , where f is frequency and i and j range over the
sensors along the line. The crosspower matrix developed in Section III for
the entire extended array was used to obtain such a matrix for each line of
senscrs. The matrix from all parallel lines of sensor were averaged to obtain
a single matrix for each of three directions for which a K-line spectra were
computed. The average matrix was then normalized so that the main diagonal
elements were unity.
The approximate spacing of the sensors forming the lines was
5 kilometers. The resulting foldover wavenumber of the spectra was . 1
cycles/km.
The K-line spectra computed for the three lines from all the
matrices generated from the 'winter' and 'summer' data in the frequency I
band . 1 to . 5 Hz are in Figure IV-16 and rV-17 respectively. Each plot consists
^ Array Research, Analysis of K-line Wavembriber Spectra from the TFO Long-Noise Sample, Special Report No. 23. ■»
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of a wavenumber power density spectrum, an integrated wavenumber power
density function, and a discrete function marked by X's which show the frac-
tional part that is unpredictable during an attempt to predict the output of the
next sensor in a line from that of the preceding ones of the line. The 0-db
level of the right hand scale for the power density spectrum is the average
value of the spectrum. The fractional scale for the integrated spectra and the
prediction error is on the right hand side. Two sets of vertical dashed lines
are shown to indicate the approximate velocity of surface mode energy either
traveling along the line or isotropic in nature (outer set) and to show the
minimum apparent velocity, of p-wave noise (inner set). The inner set of
vertical lines are not to be confused as an envelope for p-wave energy since
directional surface mode energy could also fall inside them depending on the
angle of incidence of this energy to the line of sensors.
A simultaneous analysis of the three K-line spectra at each
frequency confirms the spacial organization of the ambient noise previously
observed in the Z-dimensional wavenumber analysis. The complexity and
higher prediction of the 'winter' spectra compared to the 'summer' spectra is
due to the multiple noise sources in the 'winter' sample as previously
described.
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In the previous analysis, the direction of several definite
contributors to the ambient noise field could be determined. The integraded
wavenumber power density function was used in this study to estimate more
accurately as a function of frequency the percentage each contribution is mak-
ing to the total 'summer' and 'winter' noise level. The contributors considered
consist of 4 directional surface mode sources, Isotropie surface mode, and
P-wave as illustrated in left most part of Figure IV-18. The P-wave con-
tribution consists of any coherent energy with an apparent velocity of 8 km/sec
or greater and would be contained inside the 8 km/sec circle of the wave-
number space represented by the figure. The surface mode contributors would
be represented in wavenumber space along the circle representing the surface
mode velocity of 3. 2 km/sec. The percent of the iotal noise field which each
contributed in the two noise samples analyzed are illustrated on the right of
Figure IV-18. The most significant difference observed between the two noise
samoles is the l^rge percentage of surface mode energy in the 'winter' noise
at frequencies below . 24 Hz. This appears to be primarily due to the energy
from the direction of the Alaskan storm velocity previously discussed which
significantly increases at lower frequencies. Such a generating source of
noise should be of significant concern for longer period analysis since the
percent of contribution is rapidly increasing for the longer-period energy.
A similar observation can be made of the surface-mode energy from the
South.
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^\ -a SECTION V
MUiTTICHANNEL FILTER DESIGN AND EVALUATION ; /•
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The desirability of multichannel filtering for the extended short
period array was determined by designing and evaluating signal extraction
filters from the crosspower matrices developed in Section III. The perform-
ance of the multichannel filters'were compared to that rf the simple beam-
steering process. , . «
/ " " ■ ~ ', ' . - ■ •■
/ A. MCF DESIGN
A set of optimum Weiner multichannel filters weredesigned in
the frequency domain from each of the generated cros jpower matrices develop-
, ed fpr the 'winter' and 'summer' data. The set of MCF? from the 'winte '•
data,- denoted as MCF W, consist of 3 MCF designs, each using a subset of
the 34 array elements. The first 'Winter' MCF (MCF W-7) was designed on
the seven center elements (center seismometer Zl) plus the intermost ring of
1\ > seismometers) of the extended array. MCF W-18 was deisignecf on the same
elements as MCF W-7 plus 11 elements of the next ring of sensors (sensors
Z19and Z22 were not operating properly). The third MCF* MCF W-34, , j
includes all of the elements, except Z19, Z22, and Z3nl, i . ,—,
An equivalent set of ^MCFs developed from the 'summer' data
is denoted as MCF S-6, MCF S-17, and MCF S-33. In this case only 6, 17,
and 33 elements respectively w^re used due to one of the elements (Z-6) on -
the inner ring being bad. Figure III-l is shown to indicate the elements
actually used in each of the designs. , *•:
The signal model used in the MCF designs represented waves | ^ -^ ' 7" '" - I *
vertically incidt;nt to the extended array. The signal amplitude on each ,• " ■' ■ .>•■■. ■■;■.',,'■
channel was assumed to have a constant ratio (1) to the noise, on that channel
j . at each frequency. THe signal vector V, is thus defined such V . =yN,.where
N.. is an element of the noise crosspower matrix, N.» The signal matrix is I *■, ' ■•.ii v.c' -.H \ - :>'■■* I •-'. defined as S''- V V ." V . " ••' ... ■ „,' ■■ ,
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t The equation for the Wiener filter responses, Z, to enhapce
the signal with minimum mean square error,
[N + S] "z =(a/ri)V where (s/n) = 4.0,
was solved at each of the desired frequencies.
B. EVALUATION OF MCFs
The designed MCFs were evaluated in the frequency domain
through direct applications of the filter response, ?, to the noise matrix
from which they were designed and through an analysis of wavenumber
responses at selected frequencies. The S/N improvement obtained in the
application was compared to that obtained by simple beamsteering on the
same data. ,, ^ ' ■,
1. Signal-to-Noise Improvements-^
The sigffär-to-noise improvement for each of the MCFs was
obtained by taking ratio of the output signal-to-noise ratio, S /N , where 1 ' . ■ 0 o
\ S = VTZ 2 ' and
where
N
S./N. i i
Z NZ , to the input signal-to-noise ratio, S./N.,
1.
The signal-to-noise improvement for the set of 'winter1 and
•summer" MCFs is presented in Figufe V-l for the frequency baiid of 0.0 to
1. 25 Hzf A comparison of the two sets show that the MCF W filters obtain a
significantly higher S/N improvement below 0*75 Hz than, the equivalent MCF S
filters, as expected due to the previously observed increase of surface mode
energy in the 'winter • data sample. A maximum of 11 db more S/N improve-
ment was obtained by MCF W-34 than by MCF S-33 at the frequency of 0. 12 Hz.
'Similarly, S/N improvements were obtained for ^straight
summation process oh each of the jubset of elements. A ratio of the MCF
improvement to this summation process is shown.in Figure V-2. On the
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Signal-to-Noise Improvement Obtained by MCF Processing on 'Summer' and 'winter' Data
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Figure V-2. Signal-to-Noise Improvement of MCFs Relative to Beamsteer Processing of Similar Elements
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'stimmer' data less than 2. 0 db gain is obtained by MCF processing at
frequencies higher than 0. 8 Hzf A maximum of 5. 6 db S/N improvement over
a summation process was obtained at 0. IZ^Hz by the MCF S-33. The MCF W
set of filters show significantly more improvement over the summation. This
is due primarily to the surface mode energy, however, since less statistics
were used in the 'winter' sample than the 'summer' data some of the gain is *
false due to overdesign of the MCF. Based on a study by John Burg, et al,
resu ts from evaluating the 34 channel filter MCF W-34 on the statistics from
which it was designed will be biased approximately 1.4 db over the true opti-
mum Wiener filter performance. (122 samples, 34 channels). For the 18
channel case, MCF W-18 the evaluation will be biased only . 75 db. For the
•summer1 data 230 effective segments of data was used to generate the matrices,
thereby resulting in a 33 channel MCF with a bias of less than .7 db relative to
the Wiener with the true filter.
Allowing for the false gain of the MCFs, the improvement at
higher frequencies (above . 75 Hz) is ine-ignificant and a simple summation pro-
cess is considered adequate. The improvement obtained in the . 12 to .75 Hz
band is directly related to the increase in the surface mode noise power of the
noise sample.
C. WAVENUMBER ANALYSIS OF MCF RESPONSES
The wavenumber response of the MCFs, MCF W-34 and MCF
S-33, were computed at'several selected frequencies for comparison to the
wavenumber spectra of the noise previously discussed in Section IV.
)
[ 4
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StatisticXjffoverning the Design and Performance of Noise-Prediction Filters, - Advanced Array Research Special Report No. 3, 8 Septembpfc(^fl967.
V-5 services group
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The wavenumber respons? of MCF S-33, at the lower frequencies
of . 135 and . 169 Hz showing the k-space area being significantly rejected is
presented in Figure V-3. Response at the signal region (K=0) is approximately
.0 db. A dashed circle in the spectra represents surface mode values. Pri-
marily the MCF is working to reject the surface mode energy from the North-
east and the West-Southwest with some emphasis placed on rejecting the p-wave
energy coming from the South. There are also indications that the MCF is
attempting to reject surface mode energy from the direction of the Gulf of
Mexico to the Southeast of the array.
At two higher frequencies of .24 and . 30 Hz (Figure V-4)the
response becomes Isotropie to surface mode velocities with some emphasis on
the energy from the Southwest. The MCF continues to reject the p-wave energy
from the South-Southwest. The velocity of 16 km/second from the Southwest
is strongly i-ejected by the MCF at . 304 Hz.
Comparable wavenumber responses for the MCF W-34 is shown
in Figure V-5. At . 122 Hz the MCF is strongly rejecting the surface mode
energy from the Northwest and Southeast to obtain the 23 db signal-to-noise
improvement of Figure V-l. As the frequency is increased to .244 Hz, the
MCF begins to significantly reject the p-wave energy from the Northwest in
addition to isotropic rejection of surface mode energy. At higher frequencies
the MCF rejection of p-wave energy also becomes isotropic.
The significant difference in the 'winter1 and 'summe^' MCF is
the rejection of surface mode energy from the Northwestftit low frequencies
(. 12 to .24 Hz} and a more isotropic p-wave response at higher frequencies
(.3 to .4 Hz).
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Figure V-3. Wavenümber Response uf 'summer' MCF at Frequencies of . 135 and . 169 Hz,
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Figure V-4. 'W^venumber Response of 'summer1 MCF of . 236 and . 304 Hz.
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Figure V-5. Wavenurnb^r Responsie of 'winter1 MCF at Frequencies , of . 122 and .249 Hz.
'V-9 services group
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D. CONCLUSIONS
The performance of multichannel filtering for the extended
short-period array is highly dependent on the level of the noise. Under noisy
conditions, apparently caused by storm activity near coastlines, MCFs can
provide significant improvement over be?msteer processing at frequencies
below ,75 Hz. Above this frequency, however, very little improvement is
obtained under either condition. Since the frequencies of prime signal interest
lie in the higher frequency band and the generating sources, below . 75 Hz are
not stationary, the designed MCFs would not be useful for on-line application.
;•
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UNCLASSIFIED \ S«-i unly t'l.is'.ifu jlion
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>r. u$ltf • -'" ttUt t*ti'*n
DOCUMENT CONTROL DATA R&D JI II1U-. U.,ly ul tb-lrmcl und ,nü,*m£ «inoMfionmu.» he mnterrd »hen Ihe overall repurl .> claimed)
\im. REPOHT teCURlT» CLASSIFICATION
UnclasBified 2b CROUP |
Trr NOISE STUDV FOR TFO EXTENDED SHOP T-PERIOD ARRAY - SEISMIC ARRAY PROCESSING TECHNIQUES TECH. REPORT NO. 5
4 'tsr^ifTi/t NOTES^ TV/»«* L»' rrpott and Jnc/u»! v«» tlmt9M)
Technical ■ ' ^ AH CMQIVISI < t trsl nmmv. muUll* mitiml. Im a I nmm»)
Thomas W. Rekieta
MO*« f. D * It
22 July 1970
F33657-70-C-0100
VELA/T/0701/B/ASD
7». JOTAL NO OF PACES
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I A e S t R A c
12 SPONSORING MILI TARV ACTIVITY
Advanced Research Projects Agency Department of Defense The Pentagon. Washington, P.C. 20301 -^
Seismic da<ta was digitally collected from the recently extended short-period^ array of the Tonto Forest Observatory during the summer pf 1968 and the winter of 1969, An analysis of the data was made to characterize the ambient noise field from each period and to determine time-and space-stationarity of the fields. The effectiveness of multi-channel filter processing on the extended array was also
measured. , ' ^ ■ Several contributors to the ambient noise field could be defined in both of the
periods analyzed and appeared to be both time-and space stationary. Other contri- butors, due primarily to atmospheric storm or pressure activity, were not station- ary and could be related to H's gen«*aJting' source.
Multi-channel filtering of the extended array could not provide any significant improvement over simple beamsteering at frequencies of interest (greater than .8 H,z), At lower.frequencies, the amount of imprbvemerft obtained by MCF processing relative to beamstee ring was directly related to the increase in noise level due to •>*
•the non-stationary contributor of the.noise field, , . '
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